Abstract
Archimedes’ genius was derived in no small part from his ability to effortlessly interpret problems in both geometric and mechanical ways. We explore, in a modern context, the application of mechanical reasoning to geometric problem solving. The general form of this inherently Archimedean approach is described and it’s specific use is demonstrated with regard to the problem of finding the geodesics of a surface. Archimedes’ approach to thinking about problems may be his greatest contribution, and in that spirit we present some work related to teaching Archimedes’ ideas at an elementary level. The aim is to cultivate the same sort of creative problem solving employed by Archimedes, in young students with nascent mechanical reasoning skills.
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REFERENCES
Bendick J., Archimedes and the Door of Science, Bethlehem Books, 2009.
DeSapio V., Khatib O. and Delp S., Least action principles and their application to constrained and task-level problems in robotics and biomechanics, Multibody System Dynamics, Vol. 19, No. 3, pp. 303–322, April 2008.
Do Carmo M., Differential Geometry of Curves and Surfaces, Prentice Hall, 1976.
Gauss K.F., Über ein neues allgemeines Grundgesetz der Mechanik (On a New Fundamental Law of Mechanics), Journal für die Reine und Angewandte Mathematik, Vol. 4, pp. 232–235, 1829.
Goldstein H., Poole C. and Safko J., Classical Mechanics, 3rd ed., Addison Wesley, 2002.
Heath T., The Method of Archimedes, recently discovered by Heiberg: A supplement to the Works of Archimedes, Cosimo Classics, 2007.
Hertz H., The Principles of Mechanics Presented in a New Form, Dover, 2004.
Hirshfeld A., Eureka Man: The Life and Legacy of Archimedes, Walker & Company, New York, 2009.
Levi M., The Mathematical Mechanic: Using Physical Reasoning to Solve Problems, Princeton University Press, 2009.
Lutzen J., Mechanistic Images in Geometric Form: Heinrich Hertz’s Principles of Mechanics, Oxford University Press, 2005.
Netz R. and Noel W., The Archimedes Codex: How a Medieval Prayer Book Is Revealing the True Genius of Antiquity’s Greatest Scientist, Da Capo Press, 2009.
Westfall R.S., The Construction of Modern Science: Mechanisms and Mechanics, Cambridge University Press, 1997.
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De Sapio, V., De Sapio, R. (2010). Mechanical Advantage: The Archimedean Tradition of Acquiring Geometric Insight form Mechanical Metaphor. In: Paipetis, S., Ceccarelli, M. (eds) The Genius of Archimedes -- 23 Centuries of Influence on Mathematics, Science and Engineering. History of Mechanism and Machine Science, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9091-1_37
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DOI: https://doi.org/10.1007/978-90-481-9091-1_37
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